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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Surface Areas of Prisms and Cylinders

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Exercise 5 Page 817

Use the formula for the surface area of a cylinder.

Lateral Area: 653.5 yd^2
Surface Area: 1715.3 yd^2

Practice makes perfect

We are asked to find the lateral area and surface area of the given cylinder.

We will do these things one at a time.

Lateral Area

Let's recall the formula for the lateral area L of a right cylinder. L=2π rh Here, r is the radius of the base, and h is the height of the cylinder. Since we are given that the radius is 13yd and the height is 8 yd, we can substitute them into the formula and calculate L.

L=2 π r h

r= 13, h= 8

L=2 π ( 13)( 8)

Multiply

L=208 π

Use a calculator

L=653.451271...

Round to 1 decimal place(s)

L≈ 653.5

The lateral area of the solid is 208 π yd^2 that is approximately 653.5 yd^2.

Surface Area

Let's recall the formula for the surface area of a cylinder. S=L+2π r^2 In this formula, r is the radius of the base and L is the lateral area of the cylinder. Substituting r with 13 and L with 208 π into the formula, we can find the value of S. Let's do it!

S=L+2π r^2

r= 13, L= 208 π

S=208 π+2π( 13)^2

▼

Simplify right-hand side

Calculate power

S=208 π+2π(169)

Multiply

S=208π+338π

Add terms

S =546 π

Use a calculator

S = 1715.309588 ...

Round to 1 decimal place(s)

S≈ 1715.3

The surface area of the cylinder is about 1715.3 yd^2.

Subchapter links

Exercises p.817-821